The angle used to create the rotated PC1–PC2 coordinate system that is used in Fig. 1 was obtained by maximizing θ in the objective function: f(θ)=Cor(g(θ,v1,v2),Long)+Cor(h(θ,v1,v2),Lat) where g(θ, v1, v2) and h(θ, v1, v2) are functions that return coordinates of v1 (the PC1 eigenvector) and v2 (the PC2 eigenvector) after rotation about the point (0,0) in PC1–PC2 space by the angle θ. Lat and Long are vectors of the latitude and longitude of each individual, and Cor(·, ·) is the correlation function. The resulting optimal value of θ was found to be −16 degrees.
